Can you figure the odds at slots?

26 June 2014

By John Grochowski

On just about every casino game, the house gets its edge from paying winners less than true odds. That goes for slot games just as it does on the tables.

However, players don’t get enough information to do the math and calculate true odds. That doesn’t stop some players from trying to apply a little tallying and arithmetic of their own.

LeAnn: When we were first together my husband was determined to figure out how many symbols and spaces there are on a slot reel. He thought that if he just knew that, he could calculate which machines had better odds of winning.

LeAnn’s husband’s method was more feasible when slots were in their infancy. If a machine had one jackpot symbol on each of three reels, with 10 symbols on each reel and no other spaces for the reels to stop, then the odds of hitting the top jackpot were 1 in 10x10x10, or 1 in 1,000. With a bigger reel, the odds could grow to 1 in 20x20x20, or 1 in 8,000.

Reels could get only so big and still fit in the machine casing, so jackpot sizes were limited.

It’s a far different situation today. On video slots, reel strips aren’t confined by the size of the machine at all. They can be as long as the game designer and programmer need them to be. Trying to count symbols on a video reel is a futile exercise.

On modern games with mechanical reels, it would do you no good to know how many symbols and spaces there are on a reel. That’s because stops are mapped to a “virtual reel,” and the number of times a symbol occurs on the virtual reel doesn’t have to be proportionate to the number of times it appears on the physical reel. A reel with 40 symbols and spaces could be made to behave as if it had 64, 128, 256 or whatever number of stops were needed to yield the desired odds of the game.

To calculate odds, you’d need to know how many stops there are on the virtual reel, and how many times each symbol is mapped to it. That information is not available to players.

Barry: I was playing Wheel of Fortune, and noticed there are 22 equal spaces on the wheel. The low ones come up over and over, and you hardly ever see the big ones. Why is that?

I’ve touched on this before, but Wheel of Fortune remains a very popular theme in what has become a large family of slot games, so I get questions like Barry’s a couple of times a year. The wheel is programmed just like a slot machine reel, with numbers mapped onto a virtual wheel. I’m not privy to the exact numbers IGT uses, but I can give an example to show you how it works.

Let’s say you and I are setting up a game with a wheel divided into 22 segments, ranging from a $20 payoff to $1,000. We don’t want to be paying out $1,000 once per 22 spins, so we program a virtual wheel with 1,000 numbers. We map it so that every time our random number generator spits out number 1, the wheel stops on the $1,000 space. We map four numbers that will make the wheel stop on the $500 space, and so on until we use 100 numbers to make it stop on a $20 space.

Now instead of paying out $1,000 once per 22 spins, it will pay the grand only once per 1,000 spins. And instead of paying $20 once per 22 spins, it’ll be one out of 10.

The game is still random, but it’s skewed toward smaller payoffs.

Clarissa: I’m curious about video poker and the payoffs. It seems to me like the odds against hitting a royal flush are a lot longer than the payoff. Shouldn’t the payoff be a LOT bigger?

In video poker, we DO have enough information to do the math ourselves. Every card has an equal chance of being dealt on every deal, just as if a physical deck of cards was shuffled for every hand. That’s why we can calculate payback percentages and strategies.

The chances of drawing a royal flush range from about 1 in 40,000 to 1 in 48,000 on Jacks or Better-based games, with the variation caused by changes in player strategy to account for different pay tables.

What if games paid something very close to true odds of hitting a royal? Then the machines would have to eliminate payoffs on all other hands in order to keep overall returns to players from soaring far above 100 percent.

A game with all its payouts in rare hands would be unplayable, with extremely long losing streaks. So payoffs are apportioned among other hands so that wins are frequent enough to keep players interested.

That’s all part of the programmer’s art, paying less than true odds while giving players a good time and the feeling they have a shot to win. And it’s all in the math.


Look for John Grochowski at www.casinoanswerman.com, on Facebook (http://tinyurl.com/7lzdt44) and Twitter (@GrochowskiJ).